Polytope of Type {11,2,42}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {11,2,42}*1848
if this polytope has a name.
Group : SmallGroup(1848,147)
Rank : 4
Schlafli Type : {11,2,42}
Number of vertices, edges, etc : 11, 11, 42, 42
Order of s₀s₁s₂s₃ : 462
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {11,2,21}*924
   3-fold quotients : {11,2,14}*616
   6-fold quotients : {11,2,7}*308
   7-fold quotients : {11,2,6}*264
   14-fold quotients : {11,2,3}*132
   21-fold quotients : {11,2,2}*88
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s2 := (14,15)(16,17)(18,19)(20,21)(22,25)(23,24)(26,27)(28,31)(29,30)(32,33)
(34,37)(35,36)(38,39)(40,43)(41,42)(44,45)(46,49)(47,48)(50,53)(51,52);;
s3 := (12,28)(13,22)(14,20)(15,30)(16,18)(17,40)(19,24)(21,34)(23,32)(25,42)
(26,29)(27,50)(31,36)(33,46)(35,44)(37,52)(38,41)(39,51)(43,48)(45,47)
(49,53);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(53)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);
s1 := Sym(53)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);
s2 := Sym(53)!(14,15)(16,17)(18,19)(20,21)(22,25)(23,24)(26,27)(28,31)(29,30)
(32,33)(34,37)(35,36)(38,39)(40,43)(41,42)(44,45)(46,49)(47,48)(50,53)(51,52);
s3 := Sym(53)!(12,28)(13,22)(14,20)(15,30)(16,18)(17,40)(19,24)(21,34)(23,32)
(25,42)(26,29)(27,50)(31,36)(33,46)(35,44)(37,52)(38,41)(39,51)(43,48)(45,47)
(49,53);
poly := sub<Sym(53)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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